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ModelFitReport […]

represents a symbolic fit report obtained from functions like ModelFit .

ModelFitReport […][prop]

extracts a property from the report.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Property Access  
Best Model  
Model and Data Introspection  
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Parameters  
Fit Summary  
Diagnostic Plots  
Model Selection and Cross-Validation  
Classical Inference  
Linear-Only Properties  
Options  
ValidationSet  
Applications  
Polynomial Calibration  
See Also
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ModelFitReport […]

represents a symbolic fit report obtained from functions like ModelFit .

ModelFitReport […][prop]

extracts a property from the report.

Details

  • ModelFitReport represents a report containing model selection results, fit metrics, cross-validation results and classical inference for models fitted with ModelFit .
  • Reports can be returned from functions such as the "Report" property of ModelFit .
  • When a single model is passed to ModelFit , the report contains diagnostics for that model only.
  • When multiple models or hyperparameter ranges are given, ModelFit performs cross-validation to select the best model, and the report additionally contains cross-validation metrics, model rankings and a comparison chart.
  • Properties of a fit report are obtained from ModelFitReport […]["property"].
  • ModelFitReport […][{prop1,…}] gives several properties at once.
    • Properties
  • Best model properties include:
  • "BestModel" best fitted model
    "Expression" symbolic expression of the best model
    "Function" best fit pure function
    "TabularFunction" pure function operating on a row or list input
  • "Expression", "Function" and "TabularFunction" are only available for models with base type "Formula" or "Linear".
  • Model and data introspection properties include:
  • "Name" model type name
    "BaseType" "Linear", "Formula" or model-specific
    "Hyperparameters" hyperparameter settings of the best model
    "HyperparameterDomain" domain searched during model selection
    "HyperparameterDefaultDomain" default domain for the hyperparameters
    "Variables" variable symbols
    "ColumnNames" column names of the training data
    "ColumnVariableMap" column-to-variable mapping
    "VariableColumnMap" variable-to-column mapping
    "Schema" data type schema
    "InputSize" number of input dimensions
    "OutputSize" number of output dimensions
    "InputType" data types of input
    "OutputType" data types of output
    "Task" inferred task (e.g. "Regression")
    "Constraints" structural constraints on the model
    "Weights" weights applied to data points
  • Parameter properties include:
  • "Parameters" parameter symbols
    "ParameterNames" parameter names
    "ParameterValues" fitted parameter values
    "ParameterAssociation" parameter name-value association
    "ParameterRules" fitted values as a list of rules
    "ParameterCount" number of parameters
    "EstimatedParameterCount" number of estimated parameters
    "ParameterInitialValues" initial values used for fitting
  • "ParameterValues" is available for every trained model. The other parameter properties are only available for models with base type "Formula" or "Linear".
  • Fit summary properties include:
  • "TrainingLoss" training loss of the best model
    "CriterionFunction" loss function used for training
    "LossMetric" name of the loss metric
    "FitResiduals" difference between actual and predicted responses
    "TotalSumOfSquares" total sum of squares of the response
    "ResidualSumOfSquares" sum of squared residuals
    "MeanAbsoluteError" mean absolute error
    "MedianAbsoluteError" median absolute error
    "RootMeanSquaredError" root mean squared error
    "CoefficientOfVariation" coefficient of variation of residuals
    "TrainingTime" wall time spent training the best model
    "MemoryUsed" memory used while training the best model
  • Diagnostic plot properties include:
  • "ResidualHistogram" histogram of residuals with a fitted normal overlay
    "ResidualPlot" residuals against fitted values
    "ResidualTrendPlot" residuals against the predictor (1D inputs)
    "ProbabilityPlot" residual CDF against a normal CDF
    "QuantilePlot" residual quantiles against normal quantiles
    "ComparisonPlot" predicted versus actual response
  • Model selection and cross-validation properties include:
  • "Data" training data
    "Ordering" indices of models sorted by increasing loss
    "TotalTrainingTime" wall time training all candidates
    "TotalMemoryUsed" peak memory used during training
    "ValidationSet" validation set strategy used
    "CrossValidationData" per-candidate cross-validation results
    "CrossValidationChart" box-whisker chart of per-fold validation losses
  • "CrossValidationData" and "CrossValidationChart" are populated only when ValidationSet is not None , which is the default when multiple candidates are passed.
  • Classical inference properties (for "Linear" and "Formula"–based models) include:
  • "RSquared" coefficient of determination
    "AdjustedRSquared" adjusted for the number of parameters
    "AIC" Akaike Information Criterion
    "AICc" finite-sample corrected AIC
    "BIC" Bayesian Information Criterion
    "LogLikelihood" log-likelihood of the fit
    "EstimatedVariance" estimate of the error variance
    "ANOVA" analysis-of-variance table
    "ParameterEstimates" estimates, standard errors, t-statistics, p-values, confidence intervals
    "BestFitParameters" parameter point estimates
    "CorrelationMatrix" parameter correlation matrix
    "CovarianceMatrix" parameter covariance matrix
    "HatDiagonal" diagonal of the hat (projection) matrix
    "PredictedResponse" fitted values for the training data
    "Response" observed response values
    "StandardizedResiduals" residuals scaled by the residual standard error
    "StudentizedResiduals" residuals scaled by single-deletion error estimates
    "MeanPredictions" confidence intervals for the mean prediction
    "MeanPredictionBands" bands for the mean prediction
    "SinglePredictions" confidence intervals for a single observation
    "SinglePredictionBands" bands for a single observation
    "BestFitAround" fitted function with mean uncertainty
    "BestFitDataAround" fitted function with predictive uncertainty
    "SymbolicExpression" symbolic expression of the fit
  • Additional properties only available for models with base type "Linear" include:
  • "Basis" basis used in the fit
    "BasisFunctions" basis functions used in the fit
    "DesignMatrix" design matrix
    "CatcherMatrix" catcher matrix
    "Eigenstructure" eigenstructure of the design matrix
    "DurbinWatsonD" Durbin-Watson statistic
    "ResidualDegreesOfFreedom" residual degrees of freedom
    "CookDistances" Cook's distance influence measures
    "DFFITS" DFFITS influence measures
    "BetaDifferences" DFBETAs
    "FitDifferences" fit differences
    "CovarianceRatios" covariance ratios
    "FVarianceRatios" F variance ratios
    "SingleDeletionVariances" single-deletion variance estimates
    "VarianceInflationFactors" variance inflation factors
    "ModelSumOfSquares" model sum of squares
    "AdjustedModelSumOfSquares" adjusted model sum of squares
    "MeanAdjustedTotalSumOfSquares" mean-adjusted total sum of squares
    "MeanAdjustedPredictedResponse" mean-adjusted fitted values
    "MeanAdjustedResponse" mean-adjusted response
    "MeanResponse" response mean
    "PartialSumOfSquares" type-III sum of squares
    "SequentialSumOfSquares" type-I sum of squares

Examples

open all close all

Basic Examples  (3)

Obtain a ModelFitReport from ModelFit :

Wolfram Language code: report = ModelFit[ResourceData["Sample Data: Old Faithful Eruptions"], PolynomialModel[4], "Report"]

Extract "RSquared" and the training loss:

Wolfram Language code: report[{"RSquared", "TrainingLoss"}]

Define a selection of model candidates:

Wolfram Language code: models = { PolynomialModel[UpTo[3]], LinearModel[{x, y, x y}, {x, y}], DecisionTreeModel[], NearestModel[1 ;; 5 ;; 2] };

Fit the models on a dataset and get a report:

Wolfram Language code: report = ModelFit[{...}, models, "Report"]

Extract the best model:

Wolfram Language code: report["BestModel"]

The cross-validation chart compares all candidates:

Wolfram Language code: report["CrossValidationChart"]

Create a report from Tabular data:

Wolfram Language code: report = ModelFit[Tabular[Association["RawSchema" -> Association["ColumnProperties" -> Association["Temperature" -> Association["ElementType" -> "Real64"], "Rainfall" -> Association["ElementType" -> "Real64"], "Yield" -> Association["ElementType" -> "Real64"]], "KeyColumns" -> None, "Backend" -> "WolframKernel"], "Options" -> {}, "BackendData" -> Association["ColumnData" -> DataStructure["ColumnTable", {{TabularColumn[Association["Data" -> {{21.274363626077456, 32.638880243338534, 16.996761168217887, 30.663352835710246, 18.88030101422309, 21.21262925923419, 13.801297957058619, 11.9002324793208, 32.197362497036934, 13.138620238958067, 20.241436236298547, 21.112424770120537, 27.405749954829002, 13.307665147300776, 13.424766881234454, 20.97259531468952, 25.18424867059953, 23.26202816185207, 10.465484058357424, 16.397097814615964, 13.851736373951308, 18.32927044981313, 30.696173165707837, 32.9855949854575, 32.14478720052078, 12.651017398696625, 23.083461287345894, 34.83768765056927, 20.00837101659612, 12.72758428193846, 10.224240190287677, 12.586334627282277, 14.82690073071269, 32.395634205027555, 16.689618755172628, 31.796694480507682, 25.342370637828978, 31.210772576037208, 22.251263381886844, 18.573661910917895, 13.125532798463027, 16.427875268785666, 19.919216818502896, 32.39752194507377, 27.9455305105966, 31.8345659691948, 20.061383466930014, 13.856675506478668, 34.153026536410394, 34.207236449699984, 15.630086799263257, 16.582434431126632, 23.461831632894768, 16.03816820252392, 20.551299548385145, 34.788984802552996, 17.726487616668614, 33.28748205675713, 17.149461015021235, 15.822643777764197, 13.671147642322909, 20.472197623158312, 31.812583735185708, 16.17406055097594, 18.142207940290056, 33.21897402637236, 26.44068116195821, 21.810469194900286, 12.743885714520838, 24.395056606648915, 19.91093974334008, 23.213676738543654, 16.687082068575627, 16.44466906149443, 31.115143818819206, 12.23240892693733, 17.75638688155034, 13.764972848588622, 26.553872494639133, 18.876120690849458}, {}, None}, "ElementType" -> "Real64"]], TabularColumn[Association["Data" -> {{9.641212861989557, 60.953983058415396, 49.55857318259782, 73.08996038457877, 61.97622275627821, 71.10900557684073, 9.305672849447944, 28.628257611094178, 74.83625515113705, 7.501464391913437, 3.2921016112529733, 53.855813103884145, 85.41559030515337, 93.75933792308055, 31.794897478303994, 37.63213260921001, 36.85889833937892, 47.30996149289639, 51.53080829230618, 57.37227415718489, 98.76250929730787, 78.79585017348663, 10.295672147672574, 81.38868807229215, 84.5375407397281, 78.41964735938683, 24.20222059876447, 34.835603055882316, 54.79341551350898, 96.55274708711241, 86.54434859296872, 96.2875157486365, 17.57709919160082, 20.119406796064144, 37.288637716131554, 14.722088486050676, 50.639173907559744, 32.9886610770556, 8.441331794611418, 9.602548843183945, 78.62859077582974, 33.640710333037596, 48.697354016643104, 20.92859568303109, 13.509542960452237, 16.904440666776853, 83.73161565273561, 30.913664637940364, 7.482986030760741, 70.081801324632, 36.77832787614701, 17.166739206123083, 9.64106130404283, 8.97530293927218, 27.499282003188274, 29.619190255226325, 96.97525518824442, 30.168242584134177, 77.8111185730686, 55.70406138847546, 25.07170986373495, 20.606698465518992, 12.31988091780314, 7.9025824090340535, 82.15203413316654, 18.886118453183176, 75.38676235567362, 36.1735308819459, 12.80356948738186, 31.05967465302284, 45.73789203941334, 83.44539916208416, 20.450604094732938, 14.282053666309125, 59.07195894458954, 97.39939819145363, 46.70388514536488, 41.869309499622574, 82.49302603368773, 25.925568611194414}, {}, None}, "ElementType" -> "Real64"]], TabularColumn[Association["Data" -> {{45.08146625290131, 96.6233480166611, 59.327113825731054, 91.85825808285469, 66.5110526006169, 77.19922598453354, 32.64854973208589, 44.65511838395225, 97.86029555920695, 25.401312855755222, 39.76399699776998, 65.70393611331286, 96.33997195790113, 71.97379585713982, 42.37036288864871, 61.845611013121456, 68.64075765433721, 71.01270415338877, 44.61551122390785, 58.802402969637335, 73.9472536362927, 73.64086592981765, 63.3940898912315, 109.37841033261286, 108.53178099577192, 65.76034304590476, 61.28796183675285, 86.8539823601026, 69.9449058949058, 76.72144418429458, 63.818812477010155, 71.14487961376007, 38.20222764963004, 79.91412173098351, 56.61322306333139, 78.61082331457568, 73.48401475615992, 73.25237867553318, 50.23688599610344, 42.94680910126161, 65.92966250556978, 49.81892213265645, 66.61745558525139, 73.46390082751718, 61.61915786105258, 70.7726730860374, 81.59200223685298, 40.08401032223059, 69.20008390476359, 102.43121046909894, 47.602257741215894, 44.027561373056635, 49.4892877491449, 28.319608016089923, 54.4978507003262, 86.62962864217928, 84.34321749387686, 84.18221163933197, 73.10760517869035, 57.78664124110287, 38.66126694156958, 49.330257789525646, 64.97822415145333, 38.931114362893666, 75.56990446408443, 75.01933488318359, 87.10594545788089, 60.28558949870267, 32.83710116288238, 62.83182860809156, 62.75179120791623, 93.79015254438815, 44.173011036339744, 41.55780478724791, 95.73246924040717, 75.40492466050038, 55.19997511406876, 46.23818801202954, 100.35036661666152, 56.13170543835799}, {}, None}, "ElementType" -> "Real64"]]}}]]]] -> "Yield", PolynomialModel["Degree" -> 1], "Report"]

Compute a table with the best fit parameter properties:

Wolfram Language code: report["ParameterEstimates"]

Scope  (11)

Property Access  (1)

Fit a quadratic polynomial and create a report:

Wolfram Language code: report = ModelFit[{1.27721, 6.81118, 16.3862, 27.3172, 45.7425, 66.5466, 91.6841, 120.329, 154.991, 192.26}, PolynomialModel[2], "Report"];

Extract a single property:

Wolfram Language code: report["RSquared"]

Extract several properties at once:

Wolfram Language code: report[{"AIC", "AICc", "BIC"}]

List the available property names:

Wolfram Language code: report["Properties"]//Short

Best Model  (1)

Fit a linear model and create a report:

Wolfram Language code: report = ModelFit[{...}, PolynomialModel[1], "Report"];

Retrieve the best-fitted model:

Wolfram Language code: report["BestModel"]

Get its symbolic expression:

Wolfram Language code: report["Expression"]

Get a pure function ready to evaluate:

Wolfram Language code: report["Function"]

Or a function that takes a row or list input:

Wolfram Language code: report["TabularFunction"]

Model and Data Introspection  (1)

Fit a linear model on a tabular dataset with two predictors:

Wolfram Language code: report = ModelFit[Tabular[Association["RawSchema" -> Association["ColumnProperties" -> Association["X1" -> Association["ElementType" -> "Real64"], "X2" -> Association["ElementType" -> "Real64"], "Y" -> Association["ElementType" -> "Real64"]], "KeyColumns" -> None, "Backend" -> "WolframKernel"], "Options" -> {}, "BackendData" -> Association["ColumnData" -> DataStructure["ColumnTable", {{TabularColumn[Association["Data" -> {{0.7943069684562891, 0.7080887598055678, 0.6739770017474946, 0.5995060111777462, 0.6136177288156994, 0.5979121341211697, 0.4897163348012439, 0.4959688399555753, 0.36175361103397985, 0.09422864851800195, 0.3675710756343489, 0.7291272674850633, 0.6276739045491935, 0.6773008599376125, 0.4802276863628534, 0.7710106793403941, 0.670030496491105, 0.07729983367278592, 0.7133629193617443, 0.5190929012254231, 0.7479525718447673, 0.3207406582871113, 0.5066235805316166, 0.9734509795279178, 0.023526109681830665, 0.5759660120388694, 0.5231024775906685, 0.6902880992940914, 0.36658861678374666, 0.37241849877863986, 0.02346080789028626, 0.6785297349981696, 0.44077838418609927, 0.8047451549938156, 0.5206695069830114, 0.012775316043024176, 0.6033649280853377, 0.4257263150890953, 0.3599802094605511, 0.10901650649728412, 0.42643451794859155, 0.041841048162296834, 0.22606956282409496, 0.5037680533075941, 0.7899902038405706, 0.1335020648278502, 0.4379486408540876, 0.5478680739470048, 0.33517109453193394, 0.017116296468779657}, {}, None}, "ElementType" -> "Real64"]], TabularColumn[ Association["Data" -> {{0.9230476634675155, 0.42499115321423186, 0.37288479969978505, 0.3507374270720074, 0.6082545753835462, 0.19619284998440922, 0.5031917790600378, 0.4217592070384373, 0.2451739596655036, 0.7389472123661163, 0.15935202008896132, 0.5214688747353473, 0.7874057737586853, 0.2254462080599493, 0.32346966653261977, 0.33813249238476617, 0.041703820652366996, 0.8923328112815783, 0.9681733989279382, 0.9464717771022899, 0.44876546606335377, 0.627411992791097, 0.415550371754247, 0.7200651139244627, 0.9141492863288361, 0.17745401194963595, 0.3922212199378168, 0.44475314203091587, 0.33529090525314054, 0.04488252142354687, 0.35007984777532175, 0.5254632152232677, 0.8817942543510673, 0.3158581306052035, 0.6754707812763221, 0.6450549095198239, 0.1850501803278557, 0.931482766417933, 0.7630732904987889, 0.65640354073023, 0.3643179137286363, 0.8848103747713731, 0.9809099392752705, 0.9294715298165228, 0.713500694185788, 0.2613313038377727, 0.8393931045648171, 0.45265672472382534, 0.7120355962750355, 0.3795492556801465}, {}, None}, "ElementType" -> "Real64"]], TabularColumn[Association[ "Data" -> {{4.0908983691342895, 3.4373474949444756, 3.0425458981237674, 2.2859542022837855, 2.4949243099606684, 2.216400882128132, 3.244503153938381, 2.500518688229991, 0.9437692263395425, 3.2678029099823633, 1.925631536427386, 3.3131925691656097, 3.0841244512596164, 1.6828709274396894, 1.3297500620895106, 1.302129557925297, 2.1738934976685975, 2.510679748702334, 4.227355852707408, 3.821414396594548, 2.8227548815966474, 2.0522560237671743, 2.0799967958305903, 4.886964195157835, 2.419942529984725, 1.6218707627693312, 2.395865558591849, 1.9114879950286132, 2.0947312669319795, 0.4116252471645142, 1.470987060550402, 4.075706373070064, 2.802722100037144, 2.348126978852138, 2.419869116420164, 0.8540562158501932, 1.4925448113468731, 3.929805403547816, 2.660376622307889, 2.2338003598785994, 2.0582875836688115, 2.1184320549090625, 4.163433606803859, 3.5721792402863244, 3.215878081945034, 0.8195752117171486, 3.4471135378854214, 1.6299510492769407, 2.643434277272899, 1.066462924939963}, {}, None}, "ElementType" -> "Real64"]]}}]]]] -> "Y", PolynomialModel[1], "Report"];

Inspect the model name, hyperparameters, variables and input/output sizes:

Wolfram Language code: report[{"Name", "Hyperparameters", "Variables", "InputSize", "OutputSize"}]

View the data type schema:

Wolfram Language code: report["Schema"]

Inspect the inferred task and the column-to-variable mapping:

Wolfram Language code: report[{"Task", "ColumnVariableMap"}]

Parameters  (1)

Fit a quadratic polynomial and create a report:

Wolfram Language code: report = ModelFit[{...}, PolynomialModel[2], "Report"];

Inspect the fitted parameter values:

Wolfram Language code: report["ParameterValues"]

Or as a name-value association:

Wolfram Language code: report["ParameterAssociation"]

Or as a list of rules:

Wolfram Language code: report["ParameterRules"]

Inspect the number of parameters:

Wolfram Language code: report[{"ParameterCount", "EstimatedParameterCount"}]

Fit Summary  (1)

Fit a polynomial model on a noisy sinusoid:

Wolfram Language code: SeedRandom[123];report = ModelFit[Table[{x, Sin[x] + RandomVariate[NormalDistribution[0, 0.2]]}, {x, 0, 2 Pi, 0.1}], PolynomialModel[5], "Report"];

Inspect the training loss and the loss function used:

Wolfram Language code: report[{"TrainingLoss", "CriterionFunction", "LossMetric"}]

Inspect summary statistics of the fit:

Wolfram Language code: report[{"MeanAbsoluteError", "RootMeanSquaredError", "CoefficientOfVariation"}]

View the fit residuals:

Wolfram Language code: report["FitResiduals"]

Diagnostic Plots  (1)

Fit a linear model and create a report:

Wolfram Language code: report = ModelFit[{...}, PolynomialModel[1], "Report"];

Residual histogram with a fitted normal overlay:

Wolfram Language code: report["ResidualHistogram"]

Residuals against fitted values:

Wolfram Language code: report["ResidualPlot"]

Residuals against the predictor (1D inputs only):

Wolfram Language code: report["ResidualTrendPlot"]

Compare the residual distribution to a normal distribution:

Wolfram Language code: report[{"ProbabilityPlot", "QuantilePlot"}]

Predicted versus actual response:

Wolfram Language code: report["ComparisonPlot"]

Model Selection and Cross-Validation  (2)

Compare three candidate models on the same data:

Wolfram Language code: report = ModelFit[{...}, {PolynomialModel[3], PolynomialModel[5], FormulaModel[a Sin[x] + b Cos[x], x]}, "Report"];

View the cross-validation chart of per-fold losses:

Wolfram Language code: report["CrossValidationChart"]

Inspect per-candidate cross-validation results:

Wolfram Language code: report["CrossValidationData"]

Inspect the validation set strategy used:

Wolfram Language code: report["ValidationSet"]

Tune a model hyperparameter automatically:

Wolfram Language code: report = ModelFit[{...}, PolynomialModel["Degree" -> Automatic], "Report"];

Inspect the searched and selected hyperparameters:

Wolfram Language code: report[{"Hyperparameters", "HyperparameterDefaultDomain"}]

View the cross-validation chart of candidate degrees:

Wolfram Language code: report["CrossValidationChart"]

Classical Inference  (2)

Fit a parametric polynomial and create a report:

Wolfram Language code: report = ModelFit[{...}, PolynomialModel[2], "Report"];

View standard goodness-of-fit measures:

Wolfram Language code: report[{"RSquared", "AdjustedRSquared", "AIC", "BIC", "LogLikelihood"}]

View the analysis-of-variance table:

Wolfram Language code: report["ANOVA"]

View parameter estimates with standard errors, t-statistics, p-values and confidence intervals:

Wolfram Language code: report["ParameterEstimates"]

View the parameter correlation matrix:

Wolfram Language code: report["CorrelationMatrix"]

View confidence bands for the mean prediction and for individual observations:

Wolfram Language code: report[{"MeanPredictionBands", "SinglePredictionBands"}]

View the fitted function with its mean uncertainty:

Wolfram Language code: report["BestFitAround"]

Inference is also available for nonlinear "Formula" models:

Wolfram Language code: report = ModelFit[{...}, FormulaModel[a Exp[b t], t], "Report"];

Inspect parameter estimates of the nonlinear fit:

Wolfram Language code: report["ParameterEstimates"]

Linear-Only Properties  (1)

Fit a cubic polynomial and create a report:

Wolfram Language code: report = ModelFit[{...}, PolynomialModel[3], "Report"];

View the basis used in the fit:

Wolfram Language code: report[{"Basis", "BasisFunctions"}]

View the design matrix:

Wolfram Language code: report["DesignMatrix"] // Short

View Cook's distance influence measures:

Wolfram Language code: report["CookDistances"]//ListPlot

View the Durbin–Watson statistic for residual autocorrelation:

Wolfram Language code: report["DurbinWatsonD"]

View variance inflation factors for collinearity diagnostics:

Wolfram Language code: report["VarianceInflationFactors"]

View the eigenstructure of the design matrix:

Wolfram Language code: report["Eigenstructure"]

Options  (1)

ValidationSet  (1)

By default, multiple-candidate fits use cross-validation to select the best:

Wolfram Language code: ModelFit[{...}, {PolynomialModel[3], PolynomialModel[8]}, "Report"]["BestModel"]

Use ValidationSet None to disable cross-validation; selection then uses training loss, which favors more complex models:

Wolfram Language code: ModelFit[data, {PolynomialModel[3], PolynomialModel[8]}, "Report", ValidationSet -> None]["BestModel"]

Applications  (1)

Polynomial Calibration  (1)

Compare candidate calibration polynomials by cross-validation:

Wolfram Language code: calibrationReport = ModelFit[Tabular[Association["RawSchema" -> Association["ColumnProperties" -> Association["Voltage" -> Association["ElementType" -> "Real64"], "Reading" -> Association["ElementType" -> "Real64"]], "KeyColumns" -> None, "Backend" -> "WolframKernel"], "Options" -> {}, "BackendData" -> Association["ColumnData" -> DataStructure["ColumnTable", {{TabularColumn[Association["Data" -> {{-0.010969476166896475, 0.2756153809445084, 0.5207820922185693, 0.7382120799805829, 1.0546503217759733, 1.2194575138717634, 1.3884391045677433, 1.6033829117905498, 1.9298236690440007, 2.1595798162468003, 2.367355741269225, 2.6149295615382373, 2.8757709756995933, 3.150341716269671, 3.360699947498413, 3.5569273796855154, 3.821188866160027, 4.044329289569808, 4.341736469478583, 4.5009121623508825, 4.775050396904824, 4.920234619356804, 5.267961383451918, 5.43335374821147, 5.720402240607762, 6.004672093624466, 6.16321146501294, 6.421879659757259, 6.665247110897798, 6.902026686189424, 7.139691140772724, 7.349878040928825, 7.624102766754143, 7.866146435686653, 8.051876254983217, 8.307844845246612, 8.641181697728147, 8.701847646517464, 9.120930327367718, 9.318861415929092, 9.52196552528913, 9.760115115694656, 9.985932139714121}, {}, None}, "ElementType" -> "Real64"]], TabularColumn[Association["Data" -> {{0.38200464232946085, 1.22920283637981, 1.8871214084808126, 2.431102383486541, 3.8370701938421057, 4.136745328689834, 5.004704005622051, 5.943201058496604, 8.04503161230135, 9.208474450290996, 10.463510706895864, 12.325074493062694, 14.253163457745133, 16.530890253895745, 17.676161844800358, 19.786386858995463, 22.017825435262473, 24.336079367722263, 27.493189513965678, 28.82373837759027, 31.711583786858043, 33.492037474480455, 37.710262256890346, 39.682799310310166, 43.127856462197144, 46.91181543787276, 49.48299977606753, 52.822705440684544, 56.5752519915548, 59.714249740311345, 63.60854403514109, 67.07747132755826, 71.78988873463463, 75.71744353017456, 78.71636123670012, 83.23334305668024, 89.2952640647672, 90.56832009523615, 98.45483006078611, 102.29924398888342, 106.62476822948162, 111.1600309252503, 116.01116027231602}, {}, None}, "ElementType" -> "Real64"]]}}]]]] -> "Reading", PolynomialModel[1 | 2 | 3], "Report"]
Wolfram Language code: calibrationReport["CrossValidationChart"]

Inspect parameter estimates with confidence intervals for the selected calibration:

Wolfram Language code: calibrationReport["ParameterEstimates"]

Check that the residuals are consistent with the noise model:

Wolfram Language code: DistributionFitTest[calibrationReport["FitResiduals"], NormalDistribution[0, σ], "TestConclusion"]
Wolfram Research (2026), ModelFitReport, Wolfram Language function, https://reference.wolfram.com/language/ref/ModelFitReport.html.

Text

Wolfram Research (2026), ModelFitReport, Wolfram Language function, https://reference.wolfram.com/language/ref/ModelFitReport.html.

CMS

Wolfram Language. 2026. "ModelFitReport." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ModelFitReport.html.

APA

Wolfram Language. (2026). ModelFitReport. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ModelFitReport.html

BibTeX

@misc{reference.wolfram_2026_modelfitreport, author="Wolfram Research", title="{ModelFitReport}", year="2026", howpublished="\url{https://reference.wolfram.com/language/ref/ModelFitReport.html}", note=[Accessed: 15-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_modelfitreport, organization={Wolfram Research}, title={ModelFitReport}, year={2026}, url={https://reference.wolfram.com/language/ref/ModelFitReport.html}, note=[Accessed: 15-August-2026]}
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